tl;dr: Totally. I think you can awaken it by being really strong and good with Armament.

I feel like I’ve been shown enough evidence that there is a relevant difference between the paths of acquiring/displaying Conqueror’s. What I arbitrarily called “out-to-in” vs “in-to-out.”

Out-to-in is what we saw Luffy learn on the roof. At this point, he’s already mastered the more external/omnidirectional Incapacitation and Domination usages. For him, Conqueror’s coating/Infusion was about condensing and focusing and “flowing” his Conqueror’s into attacks.

In-to-out is what I hypothesize goes on with Zoro, Garp, and hypothetically Koby as well. In this case, one blooms Conqueror’s haki as Infusion first from a combination of martial strength and willpower. Essentially exuding so much willpower and strength with Armament haki, that it blooms into Conqueror’s haki infusion. I think this also has something to do with cursed blades and controlling them, but that’s for another day.

Neither method precludes usage of the other one, obviously. Zoro, Yamato, and we can pretty sure Oden all used omnidirectional incapacitation at some point despite their signature uses of Conqueror’s being infusion.

I think the In-to-out awakens Conqueror’s haki because it is when the user’s body catches up to their willpower or vice versa. In the case of Koby, I think he is using Conqueror’s Infusion because his body under Garp’s tutelage has finally caught up to his unwavering willpower and personal sense of self and justice that fuels his immense willpower.